The invention relates to methods for detecting rheological material properties, especially for measuring rheological parameters, eg viscosity, of fluid, flowable or elastic materials and for classifying the dynamic response of the materials on the basis of the measured parameters, and apparatus for implementing the methods.
In the motion of fluid or flowable materials (generally referred to in what follows as fluids), microscopic interactions of the fluid particles occur that affect the macroscopic response (viscosity) as internal resistance or internal friction and, for example, influence the mobility, fluidity, manipulability, etc of the fluid.
The macroscopic response of a moved fluid is quantified in particular by viscosity xcex7, which, according to equation (1), is in a relation to the force F that must be produced in order to move two parallel plates (liquid layers) of area A and interplate distance d contrary to one another with the shear velocity v:
F/A=xcex7xc2x7v/d
or
Fxcx9cxcex7v=xcex7{dot over (x)}xe2x80x83xe2x80x83(1)
At a sufficiently low shear rate v/d, xcex7 is a material constant. In this case one speaks of Newtonian viscosity or Newtonian fluids. It is known that, when a certain shear rate is exceeded, the force F no longer increases proportionally to the shear velocity v. In this case of so called non-Newtonian viscosity or non-Newtonian fluids there is thickening or thinning of shear accompanied by an increase or decrease of the necessary shear forces respectively and increase of velocity.
Description of the transition from the linear case of Newtonian viscosity to the nonlinear case of non-Newtonian viscosity and characterization of the nonlinear state are of great technical significance because thickening or thinning of shear at all shear rates relevant in practice occurs in technical operations like pumping, injection molding, extruding or stirring or in hydraulic systems like viscose couplings.
It is generally known that viscosity can be detected by different measuring arrangements, like a capillary viscosimeter, falling body viscosimeter, oscillating disk viscosimeter, etc. But measurement of the nonlinear state was very elaborate to date, or only possible with restrictions. Recording of viscosity as a function of velocity is either not possible with the known arrangements, or it is very time-consuming and offers a low measure of accuracy. Nor are there any practically usable realtime viscosity measurements for technical processes.
Another problem in handling flowing fluids is detection of position/time functions in order to determine velocity or acceleration. In principle this is possible, but the results in practical applications are of no use because the measured raw data are extremely sensitive to noise. The problems mentioned for the known methods of measurement not only affect viscosity but also related material parameters like relaxation times in a nonlinear state or energy dissipation through internal friction.
The publication by D. R. Gamota et al. in xe2x80x9cJ. Rheol.xe2x80x9d, vol. 37, 1993, p 919 ff, tells us of analysis of the viscoelastic response only of electrorheological materials using Fourier analysis of shear response signals after harmonic excitation of the material. The viscoelastic response is described as a function of the amplitude of an external high voltage.
In the publication of J. M. Reimers et al. in xe2x80x9cJournal of Rheologiexe2x80x9d, Vol. 40, 1996, p 167, rheological investigations of concentrated polystyrene solutions are described. For an evaluation of the non-linear response, measuring signals are subjected to a Fast Fourier Analysis in order to obtain a qualitative delimitation of linear and non-linear responses of the investigated material. I. M. Krieger et al. describe in xe2x80x9cRheol. Actaxe2x80x9d, Vol. 12, 1973, p 567, a rheometer for oscillation investigations with non-linear liquids, wherein a Fast Fourier Analysis is conducted for evaluating the measuring variables. U.S. Pat. No. 4,754,640 discloses a rheometer for determining the linear viscoelastic properties of liquids.
The object of the invention is to provide improved methods for detecting rheological material properties, eg viscosity, of fluid or flowable materials, allowing in particular fast and precise measurement in the linear and/or nonlinear state of the investigated material. The invention also intends to provide an apparatus for implementing the methods.
The invention is based on the idea of departing evaluation of a measured signal that characterizes the material""s response to the excitation in a conventional method of measuring viscosity (eg with an oscillating disk viscosimeter) after harmonic excitation of the material to be investigated, and instead of evaluating the measured signal by detecting its function of time and Fourier transformation in the frequency domain. The inventors have determined for the first time that, in a conventional viscosity measurement really intended only for materials in a linear or Newtonian state, further information about rheological material properties, especially in a nonlinear or non-Newtonian state, become available upon transition to the frequency domain.
Rheological material properties are all properties that characterize the internal friction and thus the flow behavior of the investigated material and their dependence on shear velocity, temperature, pressure and the like. Harmonic excitation is any form of excitation of mechanical oscillations of the mass elements of an investigated material according to a harmonic time function. This is preferably presented as a sinusoidal function, but may also be superimposition of a large number of sinusoidal functions. Harmonic excitation is preferably produced by a mechanical oscillating device that is part of a conventional oscillating disk viscosimeter for example. The measured signal characterizing the material response to the excitation is, in the case of an oscillating disk viscosimeter for example, a force (or torque) produced in the material by the mechanical oscillating device or otherwise a compressive force transmitted by the material.
The measured force variable can be a macroscopic force or a measured variable that is characteristic of the local stress or locally acting force in the material. A local force, variable, for example, can be determined on the basis of the stress optical relation by an optical measurement. As an example, it is possible to determine the intensity of the optical double refraction in the material as a function of time during mechanical excitation of the material. According to the stress optical relation, the optical double refraction is in a linear relation to the local force, so, according to the invention, evaluation of the time function of the intensity of the optical double refraction may be analogous to the evaluation of macroscopic force variables.
According to the invention, the Fourier transformation of the time function of the measured signal generates a shear spectrum, from which the parameters of a Taylor series expansion of the viscosity, linear or nonlinear response of the material, a state of shear thickening or shear thinning, nonlinear relaxation times in the material (after reverse Fourier transformation of position/time functions), velocities and/or accelerations of the mass elements of flowing fluids and/or so-called memory effects in the material can be extracted.
An apparatus according to the invention contains a device (eg oscillating disk or rotational viscosimeter) for measuring the time function of a characteristic rheological parameter, a device for Fourier transformation of the time function and/or reverse transformation, and a control and display unit for setting the operating parameters of the measuring device and data transfer from the transformation device. The measuring device can be part of a control circuit for detecting the start of transition of the material to nonlinear response or shear thickening or shear thinning.
If an optical measurement (intensity of double refraction) is made, the measuring device is modified accordingly by providing transparent excitation elements. For example, the limiting plates on the material to be investigated, by which exciting forces are to be transmitted to the material, can be produced of glass. An optical measurement presents hardware has advantages as regards measuring the time function of the forces acting in the material.
The Fourier analysis provided by the invention allows determination of the nonlinear terms of the viscosity in relation to the velocity or the frequency from the intensities of the higher harmonics of the Fourier spectra. Criteria are also given for nonlinear response of the examined fluids.
The invention is of special advantage in rheological investigations on materials with high nonlinearity even at the smallest shear rates. There are polymers, for example, that exhibit nonlinear behavior under shear. The relaxation times of the molecules in the polymer are so large that they can no longer be detected with technically feasible, low shear rates. The material goes straight into a nonlinear state (eg shear thinning). To enable determination of the shear rate at which the nonlinear response begins in these materials too, the invention foresees measuring the intensity of the overtones (components of higher frequency in the Fourier transformed shear spectrum) for different frequencies and amplitudes. It was found, for example, that the intensity of the overtone corresponding to three times the fundamental increases exponentially with the amplitude of material excitation. Therefore, when recording the dependence of the overtone intensity on the amplitude of the excitation, it is possible to deduce conditions (shear rate, amplitude) where of the third overtone. The shear rate of the onset point is determined by reverse extrapolation from the frequency and amplitude functions of the overtones is below a specified value. For the first time the invention allows determination of the transition region between so-called linear and nonlinear response in the case of samples where observation of linear response with technically feasible shear rates is difficult or not possible at all.
Methods and apparatus according to the invention possess the following advantages:
Complete characterization of nonlinear response (eg shear thickening or thinning) in the Fourier domain is possible for the first time, whereby both the amplitudes and the phases of higher harmonic components are detected. Relaxation times in states of non-equilibrium can be characterized. The shear data can be reconstructed basically free of noise and thus the velocity or acceleration response of the examined material can be analyzed. With a shear cycle it is possible to detect any number of shear rates (ie multiplex benefit), because a large number of shear velocities are always contained in a harmonic excitation. The measuring speed is high, allowing realtime viscosity measurement in nonlinear state. Memory effects can be measured, recognizable in the Fourier spectrum as intensity at even-numbered multiples of the excitation frequency.
The materials investigated by the invention comprise all fluid or flowable materials, especially fluid solutions, dispersing agents, emulsions, melts or flowable plastics. The materials investigated by the invention may also be gaseous or vaporous materials or elastic solids (eg rubber-like materials).